Certificate in Mathematical Methods (CM2)

The Certificate in Mathematical Methods (CM2) is an intensive program covering a variety of mathematical methods, with special focus on those which are applicable to real-world problems. Through the recorded lectures delegates will learn topics that are normally covered in the first two years of a university mathematics degree.

The CM2 course syllabus includes the following topics:

Advanced Calculus

  • Complex Numbers
  • Vector algebra
  • Matrix algebra
  • Ordinary differential equations
  • Infinite Series
  • Functions
  • Calculus for several variables
  • Vector calculus

Complex Variables

  • Basic Properties
  • Elementary Functions
  • Complex Differentiation
  • Complex Integration
  • Infinite Series
  • The Theory of Residues
  • Zeros of polynomials
  • Conformal Mapping

Transform Methods

  • Laplace and Fourier transforms
  • Applications

 

 

 

 

Linear Algebra

  • Linear equations
  • Vector spaces
  • Linear mappings
  • Eigenvalues and eigenvectors
  • Gram-Schmidt process

Differential Equations

  • Fourier Series
  • Variation of parameters
  • Linear ordinary differential equations
  • Non-linear ordinary differential equations

Numerical Analysis II – Finite Difference Methods

  • Parabolic equations
  • Hyperbolic equations
  • Elliptic equations

 

 

Introduction to Probability

  • Introduction
  • Random Variables
  • Continuous Random Variables
  • Multivariate Random Variables

Mathematical Methods

  • Elliptic Equations and related
  • methods
  • Mathematics of Hyperbolic
  • Equations

 

Analysis

  • Number systems
  • Continuity
  • Sequences
  • Differentiation and Integration
  • Uniform Convergence
  • Power series

Numerical Analysis I

  • Errors
  • Roots of equations
  • Interpolation
  • Numerical Linear Algebra
  • Integration
  • Differential Equations

Advanced Mathematical Methods

  • Asymptotic expansions of integrals
  • Non-linear ordinary differential
  • equations
  • Integral Equations & Boundary
  • Value Problems

 

Group Theory

  • Subgroups
  • Finite groups and Group tables
  • The groups
  • Lagrange’s theorem
  • Permutation groups
  • Isomorphism
  • Isometry and Matrix Groups
  • The Dihedral group
  • Cyclic groups
  • Direct Products and Finitely Generated Abelian Groups
  • Coset groups